The gravitational field strength at the surface of a certain neutron star is 1.34*10^12 N/kg. What would be the theoretical maximum height of a cylindrical granite column which could support its own weight without crushing when exposed to a field of this magnitude? (density of granite
To find the theoretical maximum height of a cylindrical granite column that can support its own weight without crushing in a given gravitational field, we can use the concept of pressure.
The pressure on an object due to its own weight can be calculated using the formula:
Pressure = density * gravitational field strength * height
We are given the gravitational field strength as 1.34 * 10^12 N/kg. To convert this value to kg/m^3 (the unit of density), we can divide it by the acceleration due to gravity (approximately 9.8 m/s^2):
Gravitational field strength in kg/m^3 = 1.34 * 10^12 N/kg / 9.8 m/s^2
Next, we need to know the density of granite. The density of granite varies depending on the specific type but is typically in the range of 2,600 to 2,800 kg/m^3. Let's assume a density of 2,700 kg/m^3 for our calculation.
Now we can rearrange the pressure formula to solve for height:
Height = Pressure / (density * gravitational field strength)
Substituting the values we have:
Height = (1.34 * 10^12 N/kg) / (2,700 kg/m^3 * 9.8 m/s^2)
Calculating this expression will give us the theoretical maximum height of the granite column that can support its own weight without crushing in the given gravitational field.